Pith Number

pith:PPROPMZ2

pith:2015:PPROPMZ2YBLYJFSCDMKVNXVSRZ

not attested not anchored not stored refs pending

Extensions of Positive Definite Functions: Applications and Their Harmonic Analysis

Feng Tian, Palle Jorgensen, Steen Pedersen

arxiv:1507.02547 v1 · 2015-07-09 · math.FA · math.CA · math.OA · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PPROPMZ2YBLYJFSCDMKVNXVSRZ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:37:06.399219Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7be2e7b33ac0578496421b1556deb28e7ff00e65d3b1d86b722f54ea445c69ce

Aliases

arxiv: 1507.02547 · arxiv_version: 1507.02547v1 · doi: 10.48550/arxiv.1507.02547 · pith_short_12: PPROPMZ2YBLY · pith_short_16: PPROPMZ2YBLYJFSC · pith_short_8: PPROPMZ2

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PPROPMZ2YBLYJFSCDMKVNXVSRZ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7be2e7b33ac0578496421b1556deb28e7ff00e65d3b1d86b722f54ea445c69ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6afb6a4da5e043c6bc693a5faee82c4a68a9eed8512484b3fa45dad4f739b6d7",
    "cross_cats_sorted": [
      "math.CA",
      "math.OA",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-07-09T15:16:11Z",
    "title_canon_sha256": "aa9e0cd62d96ab010617eb0261d025bb1f9212d5ac3217933b096f421a3fa40f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.02547",
    "kind": "arxiv",
    "version": 1
  }
}